NEW YORK (CNNMoney.com) -- Stocks rallied Tuesday as investors focused on the positive implications for the economy in the Federal Reserve's decision to hold interest rates steady, and on diminishing fears about AIG's solvency.

The Dow Jones industrial average (INDU) gained 1.3%. The Dow had fallen to a fresh bear market trading low of 10,742.70 in the morning before bouncing back.
The Standard & Poor's 500 (SPX) index gained 1.8% and the Nasdaq composite (COMP) added 1.3%.
After the close however, AIG shares tumbled around 50% on a report that the government is considering conservatorship as a means of rescuing the troubled insurer. The government put Fannie Mae and Freddie Mac in conservatorships earlier this month, enabling it to oversee operations and protect the assets of the two mortgage lenders.
Following the reports, AIG issued a statement saying that its life insurance, general insurance and retirement services businesses are operating normally. The insurer reiterated that it continues to look for means of raising capital to address what it says are short-term liquidity issues.
Also after the close, reports said that Barclay's has agreed to buy some of the investment banking and trading operations of Lehman Brothers, which declared bankruptcy on Monday after failing to find a buyer. Lehman (LEH, Fortune 500) shares gained 43% during the regular session.
Additionally, Morgan Stanley reported better-than-expected third-quarter sales and earnings after the close Tuesday, one day ahead of schedule.
Tuesday's market: Stocks seesawed throughout the session as investors considered the prospects for AIG, the world's largest insurer.
The company has seen its stock price and investor confidence plummet as it has struggled to raise cash amid the credit market fallout. Reports that the Treasury could step in helped the stock trim morning losses and gave the market a leg up.
Also helping Wall Street Tuesday: an ultimately positive reaction to the Fed's decision to hold the fed funds rate, a key short-term interest rate, steady at 2% - and not signal worsening conditions in its statement. Stock investors initially took a knee-jerk negative reaction to the Fed, before taking a more sanguine response.
Although a cut to the fed funds rate might have provided a psychological boost, the central bank is already providing a lot of liquidity to Wall Street, said Brian Battle, vice president at Performance Trust Capital Partners.
""That they didn't ease says that they don't think the economy has gotten worse, which is a positive,"" Battle said. ""It also says they are saving their ammunition for when they need it going forward.""
He said that the focus now is what happens to AIG. More so than Lehman Brothers, AIG represents a bigger threat to the financial system because of the depth of its business.
""If you want to talk about a domino, this is a domino,"" Battle said.
Much like Freddie Mac and Fannie Mae, which the government stepped in to save last week, AIG may be too big to fail, Battle said.